Which do you think is the best Civ to go for? I've tried Hungary, Rome and Sumeria so far.
I'm interested in the effect of game speed on the game. Am I right in thinking the faster the speed the harder a domination victory? Hence is the faster the speed the easier a non military victory because that makes withstanding the early onslaught easier? I usually play quick or standard for the sake of my relationship.
For which civ, that question is kind of impossible to answer without more context.
Early rush, general ease of playing, potential power - different civs have different answers.
For early rush, Sumeria is obviously one of the strongest candidates in the game, and the strongest of the ones you listed.
You do have to be successful in that rush though and use the early city advantage (cities you conquered) to snowball your game, as you otherwise have no real bonuses to help for domination.
"Potential power" however is Byzantium hands down, for me at least, while also being generally easy to play if you know what you're doing.
As long as you are comfortable in setting up a religion on Deity without dying, Byzantium is ridiculously strong, and just keeps growing in strength.
You have so many modifiers upon modifiers (taxis, crusade, tagma adjacency), and your biggest speed bump (walls) does not exist.
Speaking of easy to play, Gaul isn't too bad.
Generally useful combat bonus that comes into play early and stays relevant, your warrior UU can keep engaging swordsmen making it more forgiving when the AI techs up, and there is the stupid Man at arms-rush you can pull off in the early classical era to reach a strong power spike.
Speed affects the game to a very large degree, and yes, domination becomes a lot easier the slower the game is, and non-domination games also become easier the faster the game is.
The reason is that the time for teching up (into new units) is dependent on game speed, whereas the actual units themselves behave the same regardless of speed.
Which is especially important in getting your domination snowball to roll, as the hardest part about domination on Deity is to conquer your first neighbour early.
The Deity AI generally techs walls and classical/medieval units so fast, that you have a
very limited window to conquer his first few cities.
You extend this window by having slower game speed, because once your units are out, they will move like usual, allowing them to reach the AI (and do their thing) while the AI still techs up.
Contrast this to faster speeds, and the AI has most likely already teched up before you reach him, getting those walls and units out, making your warriors struggle just that much more.
As you problably already know, and assuming you use warriors, the difference between attacking an unwalled city with 20 combat strength, and a city with walls and 35 combat strength is like night and day.